Table 1 The errors and convergence rates of \(\pmb{u-u^{hk}}\) in the \(\pmb{L^{2}}\) and \(\pmb{H^{1}}\) norms concerning h at \(\pmb{t=1}\)
From: Convergence of a space-time continuous Galerkin method for the wave equation
h | Error in \(\boldsymbol{L^{2}}\) | Rate | Error in \(\boldsymbol{H^{1}}\) | Rate |
|---|---|---|---|---|
1/8 | 4.8975e − 2 |  | 1.6055e − 0 |  |
1/16 | 1.2272e − 2 | 1.9967 | 8.0820e − 1 | 0.9902 |
1/32 | 3.0747e − 3 | 1.9968 | 4.0534e − 1 | 0.9956 |
1/64 | 7.6265e − 4 | 2.0113 | 2.0206e − 2 | 1.0043 |